Quantum theory of spin waves in finite chiral spin chains

We calculate the effect of spin waves on the properties of finite-size spin chains with a chiral spin ground state observed on biatomic Fe chains deposited on iridium(001). The system is described with a Heisenberg model supplemented with a Dzyaloshinskii-Moriya coupling and a uniaxial single ion anisotropy that presents a chiral spin ground state. Spin waves are studied using the Holstein-Primakoff boson representation of spin operators. Both the renormalized ground state and the elementary excitations are found by means of Bogoliubov transformation, as a function of the two variables that can be controlled experimentally, the applied magnetic field and the chain length. Three main results are found. First, because of the noncollinear nature of the classical ground state, there is a significant zero-point reduction of the ground-state magnetization of the spin spiral. Second, there is a critical external field from which the ground state changes from chiral spin ground state to collinear ferromagnetic order. The character of the two lowest-energy spin waves changes from edge modes to confined bulk modes over this critical field. Third, in the spin-spiral state, the spin-wave spectrum exhibits oscillatory behavior as function of the chain length with the same period of the spin helix.

Imaging of spin waves in atomically designed nanomagnets

The spin dynamics of all ferromagnetic materials are governed by two types of collective phenomenon: spin waves and domain walls. The fundamental processes underlying these collective modes, such as exchange interactions and magnetic anisotropy, all originate at the atomic scale. However, conventional probing techniques based on neutron1 and photon scattering2 provide high resolution in reciprocal space, and thereby poor spatial resolution. Here we present direct imaging of standing spin waves in individual chains of ferromagnetically coupled S = 2 Fe atoms, assembled one by one on a Cu2N surface using a scanning tunnelling microscope. We are able to map the spin dynamics of these designer nanomagnets with atomic resolution in two complementary ways. First, atom-to-atom variations of the amplitude of the quantized spin-wave excitations are probed using inelastic electron tunnelling spectroscopy. Second, we observe slow stochastic switching between two opposite magnetization states3, 4, whose rate varies strongly depending on the location of the tip along the chain. Our observations, combined with model calculations, reveal that switches of the chain are initiated by a spin-wave excited state that has its antinodes at the edges of the chain, followed by a domain wall shifting through the chain from one end to the other. This approach opens the way towards atomic-scale imaging of other types of spin excitation, such as spinon pairs and fractional end-states5, 6, in engineered spin chains.

Topological spin waves in the atomic-scale magnetic skyrmion crystal

We study the spin waves of the triangular skyrmion crystal that emerges in a two-dimensional spin lattice model as a result of the competition between Heisenberg exchange, Dzyalonshinkii–Moriya interactions, Zeeman coupling and uniaxial anisotropy. The calculated spin wave bands have a finite Berry curvature that, in some cases, leads to non-zero Chern numbers, making this system topologically distinct from conventional magnonic systems. We compute the edge spin-waves, expected from the bulk-boundary correspondence principle, and show that they are chiral, which makes them immune to elastic backscattering. Our results illustrate how topological phases can occur in self-generated emergent superlattices at the mesoscale.

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No abstract.

Coral communities exposed to differential large amplitude internal waves cooling and a severe heat stress in 2010 in the Andaman Sea

Tropical scleractinian corals are particularly vulnerable to global warming as elevated sea surface temperatures (SST) disrupt the delicate balance between the coral host and their algal endosymbionts, leading to symbiont expulsion, mass bleaching and mortality. While satellite sensing of SST has proven a good predictor of coral bleaching at the regional scale, there are large deviations in bleaching severity and mortality on the local scale, which are only poorly understood. Here, we show that internal waves play a major role in explaining local coral bleaching and mortality patterns in the Andaman Sea. In spite of a severe region-wide SST anomaly in May 2010, frequent upslope intrusions of cold sub-pycnocline waters due to breaking large amplitude internal waves (LAIW) alleviated heating and mitigated coral bleaching and mortality in shallow LAIW-exposed waters. In LAIW-sheltered waters, by contrast, bleaching susceptible species suffered severe bleaching and total mortality. These findings suggest that LAIW, which are ubiquitous in tropical stratified waters, benefit coral reefs during thermal stress and provide local refugia for bleaching susceptible corals. The swash zones of LAIW may thus be important, so far overlooked, conservation areas for the maintainance of coral diversity in a warming climate. The consideration of LAIW can significantly improve coral bleaching predictions and can provide a valuable tool for coral reef conservation and management.

San Diego region historic wave and sea level data report : Coast of California Storm and Tidal Waves Study /

Mode of access: Internet.

Sedimentation in submarine canyons in San Diego County, California, 1984-1987 : Coast of California storm and tidal waves study /

Mode of access: Internet.

San Diego region wind transport and wave overwash report : Coast of California Storm and Tidal Waves Study /

Mode of access: Internet.

1982-1983 shoreline position study : Coast of California storm and tidal waves study /

Mode of access: Internet.

Shoreline movement investigations report : Portuguese Point to the Mexican border (1852-1982) : Coast of California storm and tidal waves study /

Mode of access: Internet.

State of the Coast Report, San Diego Region : Coast of California Storm and Tidal Waves Study, Volume II-Appendices-Final.

Final report.

Interaction of waves and currents /

This report presents an overview of wave-current interacion, including comprehensive review of references to significant U.S. and foreign literature available through December 1981. Specific topics under review are the effects of horizontally and vertically varying currents on waves, wave refraction by currents, dissipation and turbulence, small- and medium-scale currents, caustics and focusing, and wave breaking. The results of the review are then examined for engineering applications. The most appropriate general-purpose computer program to include wave-current interaction is the Dutch Rijkswaterstaat program CREDIZ, which is based on a parabolic wave equation. Further applications include wave and current forces on structures and possibly sediment transport. The report concludes with a brief state-of-the-art review of wave-current interaction and a list of topics needing further research and development.